论文标题
聚类对硬右等试剂三角形流体的定向特性的影响
Effect of clustering on the orientational properties of a fluid of hard right isosceles triangles
论文作者
论文摘要
最近的研究表明，坚硬的右三角形的流体具有四倍和准四倍（时期）定向对称性。然而，基于两体相关性的二维各向异性流体的标准密度功能理论，以及纳入三体相关性的扩展，无法描述这些对称性。为了解释时状对称性的起源，我们假定强粒子聚类是至关重要的成分。我们使用缩放的粒子理论来分析硬右三角形和正方形的四个二进制混合物，其中三个是单组分流体的极端模型，其中右三角形可以作为单体实体以及三角形二聚体，方形二聚体或方形四聚体存在。相图表现出丰富的现象学，具有分解和三相共存。更重要的是，在某些情况下，三角形的定向分布函数在相对粒子角度0，$π/2，$和$π$下具有同样高的峰，信号四倍，四倍，四阶，但也位于$π/4 $和$3π/4 $的次级峰，八倍的特征。另外，我们将二元混合模型扩展到由四种类型的簇组成的第四纪混合物：单体，三角形和方形二聚体以及方形四聚体。在固定簇分数的限制下，使用缩放粒子理论分析了这种混合物。除了四聚体促进的明显的四阶段外，我们发现，对于某些群集组成，单体的总取向分布函数可以表现出Quasi-eightFold（八倍）对称性。这项研究提供了群集在某些二维流体中的特殊定向特性的重要性。
Recent studies have shown the fluid of hard right triangles to possess fourfold and quasi-eightfold (octatic) orientational symmetries. However, the standard density-functional theory for two-dimensional anisotropic fluids, based on two-body correlations, and an extension to incorporate three-body correlations, fail to describe these symmetries. To explain the origin of octatic symmetry we postulate strong particle clustering as a crucial ingredient. We use Scaled Particle Theory to analyze four binary mixtures of hard right triangles and squares, three of them being extreme models for a one-component fluid, where right triangles can exist as monomeric entities together with triangular dimers, square dimers or square tetramers. Phase diagrams exhibit a rich phenomenology, with demixing and three-phase coexistences. More important, under some circumstances the orientational distribution function of triangles has equally high peaks at relative particle angles 0, $π/2,$ and $π$, signalling fourfold, tetratic order, but also secondary peaks located at $π/4$ and $3π/4$, a feature of eightfold, octatic order. Also, we extend the binary mixture model to a quaternary mixture consisting of four types of clusters: monomers, triangular and square dimers, and square tetramers. This mixture is analyzed using Scaled Particle Theory under the restriction of fixed cluster fractions. Apart from the obvious tetratic phase promoted by tetramers, we found that, for certain cluster compositions, the total orientational distribution function of monomers can exhibit quasi-eightfold (octatic) symmetry. The study gives evidence on the importance of clustering to explain the peculiar orientational properties of liquid-crystal phases in some two dimensional fluids.
